This site is supported by donations to The OEIS Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321334 n such that all n - s are squarefree numbers where s is a squarefree number in range n/2 <= s < n. 0
2, 3, 4, 5, 6, 7, 8, 12, 13, 16, 36 (list; graph; refs; listen; history; text; internal format)



The following is a quotation from Hage-Hassan in his paper (see Link below). "The (concept of) right and left symmetry is fundamental in physics. This incites us to ask whether this symmetry is in (the) primes. Find the numbers n with a + a' = n. a, a' are primes and {a} are all the primes with: n/2 <= a < n and n = 2,3, ..."

This sequence is analogous to A320447. Instead of the sequence of primes it uses the sequence of squarefree numbers (A005117). It is conjectured that the sequence is finite and full.


Table of n, a(n) for n=1..11.

Mehdi Hage-Hassan, An elementary introduction to Quantum mechanic, hal-00879586 2013 pp 58.


a(10)=16, because the squarefree numbers s in the range 8 <= s < 16 are {10, 11, 13, 14, 15}. Also the complementary set {6, 5, 3, 2, 1} has all its members practical numbers. This is the 10th occurrence of such a number.


plst[n_] := Select[Range[Ceiling[n/2], n-1], SquareFreeQ]; lst={}; Do[If[plst[n]!={}&&AllTrue[n-plst[n], SquareFreeQ], AppendTo[lst, n]], {n, 1, 10000}]; lst


Cf. A005117, A320447.

Sequence in context: A032972 A210585 A240082 * A238084 A211202 A066418

Adjacent sequences:  A321331 A321332 A321333 * A321335 A321336 A321337




Frank M Jackson, Dec 18 2018



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)